I Question about Mercury's orbit discrepancy

In the link given below, it is explained how general relativity predicts the correct results. However I am curious about the answer of the following hypothetical scenario. Let us assume that we replaced gravity with the electromagnetic force. Then the force of attraction would be the same, and mercury would be negatively charged and the sun positively charged. The question is, would the same discrepancy occur?

No. It is the distortion of space-time that causes the orbit of Mercury to slowly precess around the Sun differently than expected. Gravity and the distortion of space-time go hand-in-hand. That is not true with electromagnetic force. So that would not happen with a force like electromagnetic force.

PS. There is some precession expected due to gravity from other planets even without GR, but the amount would not be correct.

No. It is the distortion of space-time that causes the orbit of Mercury to slowly rotate around the Sun. Gravity and the distortion of space-time go hand-in-hand. That is not true with electromagnetic force. So that would not happen with a force like electromagnetic force.

The way I see it is that the distortion of space-time is a result of generalizing SR into the geometry of spacetime. This means that Mercury experiences more "relativistic effects". So does not the electromagnetic force also cause relativistic effects? As far as I know you need a larger force to accelerate a faster moving object due to relativistic effects, and that would be the case for electromagnetism.

What is different about the relativistic effects in space-time and the relativistic effects of electromagnetism, which causes only space time to cause the discrepancy?

Although in classical physics the electric attraction force has the same inverse square law as gravity, that's where the similarity ends. With gravity, all objects fall at the same rate independent of their mass and this is described using the curvature of spacetime. It is not true that all charges move at the same rate in an electric field.

The way I see it is that the distortion of space-time is a result of generalizing SR into the geometry of spacetime. This means that Mercury experiences more "relativistic effects". So does not the electromagnetic force also cause relativistic effects? As far as I know you need a larger force to accelerate a faster moving object due to relativistic effects, and that would be the case for electromagnetism.

What is different about the relativistic effects in space-time and the relativistic effects of electromagnetism, which causes only space time to cause the discrepancy?

You have the cause and effect switched. Mass causes the distortion of space-time. The easiest way to observe and measure the distortion is gravity, which is directly caused by the distortion. Electromagnetic force is not the same.

Although in classical physics the electric attraction force has the same inverse square law as gravity, that's where the similarity ends. With gravity, all objects fall at the same rate independent of their mass and this is described using the curvature of spacetime. It is not true that all charges move at the same rate in an electric field.

If charge increase as the sum of many point charges, it will also fall accelerate at the same rate.

If i recall correctly when I studied the derivation of E=mc^2 it seemed that it was based on assuming that mass is fundamentally a sum (integral).

So the fact that all objects has the same acceleration is in fact in itself not a proof of that space-time has to be curved. It could just be that all mass is a sum of different similarly quantized components.

You have the cause and effect switched. Mass causes the distortion of space-time. The easiest way to observe and measure the distortion is gravity, which is directly caused by the distortion. Electromagnetic force is not the same.

I do know that. But that does not explain why the relativistic effects of electromagnetism would not cause the same discrepancy as gravity does. When generalizing SR into electromagnetism, should not that also predict something different than newtons laws?

The reason electromagnetism doesn't need modification to work with relativity is that we never had a non-relativistic version of electromagnetic theory. We did have a non-relativistic theory of gravity, which did need an update.

The reason electromagnetism doesn't need modification to work with relativity is that we never had a non-relativistic version of electromagnetic theory. We did have a non-relativistic theory of gravity, which did need an update.

I see, but that still does not explain why my hypothetical scenario would not predict the same discrepancy? Spacetime seems to say that when the force is larger, time is slower. If we consider a spaceship in high relative motion, electromagnetic interactions are also slower. Then when the electromagnetic force accelerates the hypothetically charged mercury, then time should be slower too? Then why do they not predict the same?

Gravity is not a force in general relativity. Curvature of spacetime is all there is to gravity - planets orbit stars because the "shape" of spacetime makes that their "straight line path" (called a geodesic in curved spacetime). Electromagnetism is a force and is not related to spacetime curvature. Loosely speaking, Mercury's orbit is not quite what Newton would predict because spacetime is curved near massive bodies and geometry doesn't work the way Newton assumed. The shape of the orbit is slightly distorted compared to the Newtonian prediction as a result.

Gravity is not a force in general relativity. Curvature of spacetime is all there is to gravity - planets orbit stars because the "shape" of spacetime makes that their "straight line path" (called a geodesic in curved spacetime). Electromagnetism is a force and is not related to spacetime curvature. Loosely speaking, Mercury's orbit is not quite what Newton would predict because spacetime is curved near massive bodies and geometry doesn't work the way Newton assumed. The shape of the orbit is slightly distorted compared to the Newtonian prediction as a result.

Time dilation has nothing to do with force, by the way.

Similarly the hypothetical scenario of switching gravity with electromagnetic fields also predicts different motion. Because, when Mercury has a large momentary velocity, it accelerates slower. For the same reason why throwing a bottle (throwing bottle is electromagnetic interaction) in a rocket moving at the same speed would be slower too. This is something Newton's laws alone cannot explain. So why is it not the same difference from newtons law as GR predicts?

Because electromagnetism and gravity are different phenomena that work in different ways. Electromagnetism doesn't involve spacetime curvature (or, at least, is not mediated by it) but gravity does.

The special relativistic effects you are talking about aren't enormously impotant here because Mercury isn't moving very fast with resect to the Sun.

A charged Sun would, in fact, cause spacetime curvature because of its mass. But that's a separate issue from what I think you're trying to get at.

The electric field density should be stronger too corresponding to the strength in curvature of spacetime. Are there any experiments which proves that spacetime causes matter to behave differently than electromagnetic fields?

Staff: Mentor

The electric field density should be stronger too corresponding to the strength in curvature of spacetime. Are there any experiments which proves that spacetime causes matter to behave differently than electromagnetic fields?

Whenever we observe that the force of gravity is proportional to the mass and always attractive whereas electromagnetic forces are proportional to the charge and may be repulsive, we're confirming that difference.

However, this thread has moved into personal theorizing which is not allowed under thehysics forums rules, so it is closed. Questions about what physics does say about electromagnetism and gravity are welcome, but speculation about alternatives are not.